Extended Fermi-Dirac and Bose-Einstein functions with applications to the family of zeta functions
M. Aslam Chaudhry, Asghar Qadir, Asifa Tassaddiq · arXiv (Cornell University) · 2010
Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relation to the family of zeta functions. These extensions are "dual" to each other in a sense that is explained. Some identities are proved for them and the relation between them and the general Hurwitz-Lerch zeta function (\\phi(z,s,v) is exploited to deduce new identities.